CHICAGO — Jody A. Geiger’s July 2025 Hubble paper organizes two proposed expansion-rate realizations around a common baseline near 70.885 kilometres per second per megaparsec. The same age normalization enters the calculated lower rate, 68.261, and upper rate, 73.510, in those units. These are related outputs of one theoretical construction, not three independently measured expansion rates.

The paper, published July 22, 2025 in AIP Advances, identifies the baseline with the inverse of its adopted universe age after conversion to astronomical rate units. In a rounded-input reconstruction, an age of 13.794 billion years gives a baseline of 70.885328 in those units. Dimensionless multipliers near 0.962973 and 1.037027 produce the lower and upper values. Figure 1 identifies the calculation stages.

The common baseline makes the calculation traceable. Changing the age rescales both branches together. Their ratio removes that common age factor, while their midpoint returns the inverse-age baseline. These relationships are algebraic consequences of the same two rate definitions; they do not supply additional independent confirmations.

The baseline is a model prescription. Spatial flatness alone does not make the present Hubble rate the inverse cosmic age in a general cosmology. The age–rate relation depends on the expansion history, and connecting MQ’s construction to observations requires a defined model of distances and the underlying observables.

MQ associates the lower branch with CMB-based inference and the upper branch with Cepheid-calibrated distance-ladder inference. Those assignments are the author’s physical interpretation. Neither observational collaboration independently identified an MQ frame, and the historical numerical matches do not isolate the proposed mechanism.

The 2025 article’s comparison and calibration are retained as historical evidence. Later revised MQ values, observational datasets and uncertainty qualifications have their own versions. They should not be blended into a claim that the original paper already contained those later tests.

The companion technical Brief walks through the age conversion, inverse-second baseline, astronomical unit conversion and two dimensionless multipliers. It reproduces the historical displayed rates under stated rounded inputs, charts their shared age dependence and distinguishes that arithmetic from the proposed physical interpretation.

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